RND estimation stability with respect to methodology : A study on the EURO STOXX 50 index around the September 2008 stock market crash

Abstract: The aim of this study is to investigate whether implied RND functions are stable with respect to the choice of estimation methodology and whether the stability is affected by the stock market crash of September 15 2008. In order to do so, I estimate RND functions for the EURO STOXX 50 equity index using two different methods, namely the fully parametric two-lognormal method and a curve-fitting method based on the approach proposed by Shimko (1993). For the estimated RND functions, the mean, standard deviation, skewness and kurtosis are calculated. I find that though the qualitative shape and the direction of the evolution over time of the RND functions obtained with the two different methods are relatively similar for most of the estimated trading days, the calculated descriptive statistics show noticeable and systematic differences. These conclusions are largely unaffected by the stock market crash, though the discrepancy in the estimated skewness increases in magnitude and becomes more volatile after it. Based on this, I find that the question of whether the RND estimation is stable with respect to methodology depends on the intended application. If the aim is to qualitatively assess changes in market sentiment over time, both methods lead to largely the same conclusions, and thus, the RND can be considered stable. If, on the other hand, the RND is to be used to price a contingent claim and high numerical accuracy is necessary, the RND estimation cannot be said to be stable with respect to methodology.